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Deep Learning/Attention Mechanisms

Sotiris Anagnostidis, Dario Pavllo, Luca Biggio, Lorenzo Noci, Aurelien Lucchi, Thomas Hofmann

Autoregressive Transformers adopted in Large Language Models (LLMs) are hard to scale to long sequences. Despite several works trying to reduce their computational cost, most of LLMs still adopt attention layers between all pairs of tokens in the sequence, thus incurring a quadratic cost. In this study, we present a novel approach that dynamically prunes contextual information while preserving the model's expressiveness, resulting in reduced memory and computational requirements during inference. Our method employs a learnable mechanism that determines which uninformative tokens can be dropped from the context at any point across the generation process. By doing so, our approach not only addresses performance concerns but also enhances interpretability, providing valuable insight into the model's decision-making process. Our technique can be applied to existing pre-trained models through a straightforward fine-tuning process, and the pruning strength can be specified by a sparsity parameter. Notably, our empirical findings demonstrate that we can effectively prune up to 80\% of the context without significant performance degradation on downstream tasks, offering a valuable tool for mitigating inference costs. Our reference implementation achieves up to $2\times$ increase in inference throughput and even greater memory savings.

Deep Learning/Attention Mechanisms

Xing Han, Tongzheng Ren, Tan Nguyen, Khai Nguyen, Joydeep Ghosh, Nhat Ho

Transformer-based architectures have recently exhibited remarkable successes across different domains beyond just powering large language models. However, existing approaches typically focus on predictive accuracy and computational cost, largely ignoring certain other practical issues such as robustness to contaminated samples. In this paper, by re-interpreting the self-attention mechanism as a non-parametric kernel density estimator, we adapt classical robust kernel density estimation methods to develop novel classes of transformers that are resistant to adversarial attacks and data contamination. We first propose methods that down-weight outliers in RKHS when computing the self-attention operations. We empirically show that these methods produce improved performance over existing state-of-the-art methods, particularly on image data under adversarial attacks. Then we leverage the median-of-means principle to obtain another efficient approach that results in noticeably enhanced performance and robustness on language modeling and time series classification tasks. Our methods can be combined with existing transformers to augment their robust properties, thus promising to impact a wide variety of applications.

Deep Learning/Attention Mechanisms

Zhen Qin, Songlin Yang, Yiran Zhong

Transformers have surpassed RNNs in popularity due to their superior abilities in parallel training and long-term dependency modeling.Recently, there has been a renewed interest in using linear RNNs for efficient sequence modeling.These linear RNNs often employ gating mechanisms in the output of the linear recurrence layer while ignoring the significance of using forget gates within the recurrence. In this paper, we propose a gated linear RNN model dubbed Hierarchically Gated Recurrent Neural Network (HGRN), which includes forget gates that are lower bounded by a learnable value. The lower bound increases monotonically when moving up layers. This allows the upper layers to model long-term dependencies and the lower layers to model more local, short-term dependencies. Experiments on language modeling, image classification, and long-range arena benchmarks showcase the efficiency and effectiveness of our proposed model. The source code is available at https://github.com/OpenNLPLab/HGRN.

Deep Learning/Attention Mechanisms

Zichang Liu, Aditya Desai, Fangshuo Liao, Weitao Wang, Victor Xie, Zhaozhuo Xu, Anastasios Kyrillidis, Anshumali Shrivastava

Large language models(LLMs) have sparked a new wave of exciting AI applications. Hosting these models at scale requires significant memory resources. One crucial memory bottleneck for the deployment stems from the context window. It is commonly recognized that model weights are memory hungry; however, the size of key-value embedding stored during the generation process (KV cache) can easily surpass the model size. The enormous size of the KV cache puts constraints on the inference batch size, which is crucial for high throughput inference workload. Inspired by an interesting observation of the attention scores, we hypothesize the persistence of importance: only pivotal tokens, which had a substantial influence at one step, will significantly influence future generations. Based on our empirical verification and theoretical analysis around this hypothesis, we propose scissorhands, a system that maintains the memory usage of the KV cache at a fixed budget without finetuning the model. In essence, Scissorhands manages the KV cache by storing the pivotal tokens with a higher probability. We validate that scissorhands reduces the inference memory usage of the KV cache by up to 5$\times$ without compromising model quality. We further demonstrate that scissorhands can be combined with 4-bit quantization, traditionally used to compress model weights, to achieve up to 20$\times$ compression.

Deep Learning/Attention Mechanisms

Benjamin Hoover, Yuchen Liang, Bao Pham, Rameswar Panda, Hendrik Strobelt, Duen Horng Chau, Mohammed Zaki, Dmitry Krotov

Our work combines aspects of three promising paradigms in machine learning, namely, attention mechanism, energy-based models, and associative memory. Attention is the power-house driving modern deep learning successes, but it lacks clear theoretical foundations. Energy-based models allow a principled approach to discriminative and generative tasks, but the design of the energy functional is not straightforward. At the same time, Dense Associative Memory models or Modern Hopfield Networks have a well-established theoretical foundation, and allow an intuitive design of the energy function. We propose a novel architecture, called the Energy Transformer (or ET for short), that uses a sequence of attention layers that are purposely designed to minimize a specifically engineered energy function, which is responsible for representing the relationships between the tokens. In this work, we introduce the theoretical foundations of ET, explore its empirical capabilities using the image completion task, and obtain strong quantitative results on the graph anomaly detection and graph classification tasks.

Deep Learning/Attention Mechanisms

Zhenyu Zhang, Ying Sheng, Tianyi Zhou, Tianlong Chen, Lianmin Zheng, Ruisi Cai, Zhao Song, Yuandong Tian, Christopher Ré, Clark Barrett 等

Large Language Models (LLMs), despite their recent impressive accomplishments, are notably cost-prohibitive to deploy, particularly for applications involving long-content generation, such as dialogue systems and story writing. Often, a large amount of transient state information, referred to as the $\mathsf{KV}$ $\mathsf{cache}$, is stored in GPU memory in addition to model parameters, scaling linearly with the sequence length and batch size. In this paper, we introduce a novel approach for implementing the $\mathsf{KV}$ $\mathsf{cache}$ which significantly reduces its memory footprint. Our approach is based on the noteworthy observation that a small portion of tokens contributes most of the value when computing attention scores. We call these tokens Heavy Hitters ($\mathsf{H_2}$). Through a comprehensive investigation, we find that ($i$) the emergence of $\mathsf{H_2}$ is natural and strongly correlates with the frequent co-occurrence of tokens in the text, and ($ii$) removing them results in significant performance degradation. Based on these insights, we propose Heavy Hitter Oracle ($\mathsf{H_2O}$), a $\mathsf{KV}$ $\mathsf{cache}$ eviction policy that dynamically retains a balance of recent and $\mathsf{H_2}$ tokens. We formulate the $\mathsf{KV}$ $\mathsf{cache}$ eviction as a dynamic submodular problem and prove (under mild assumptions) a theoretical guarantee for our novel eviction algorithm which could help guide future work. We validate the accuracy of our algorithm with OPT, LLaMA, and GPT-NeoX across a wide range of tasks. Our implementation of $\mathsf{H_2O}$ with 20\% heavy hitters improves the throughput over three leading inference systems DeepSpeed Zero-Inference, Hugging Face Accelerate, and FlexGen by up to $29\times$, $29\times$, and $3\times$ on OPT-6.7B and OPT-30B. With the same batch size, $\mathsf{H_2O}$ can reduce the latency by up to $1.9\times$.

Deep Learning/Attention Mechanisms

Zhenchao Jin, Xiaowei Hu, Lingting Zhu, Luchuan Song, Li Yuan, Lequan Yu

Co-occurrent visual patterns suggest that pixel relation modeling facilitates dense prediction tasks, which inspires the development of numerous context modeling paradigms, \emph{e.g.}, multi-scale-driven and similarity-driven context schemes. Despite the impressive results, these existing paradigms often suffer from inadequate or ineffective contextual information aggregation due to reliance on large amounts of predetermined priors. To alleviate the issues, we propose a novel \textbf{I}ntervention-\textbf{D}riven \textbf{R}elation \textbf{Net}work (\textbf{IDRNet}), which leverages a deletion diagnostics procedure to guide the modeling of contextual relations among different pixels. Specifically, we first group pixel-level representations into semantic-level representations with the guidance of pseudo labels and further improve the distinguishability of the grouped representations with a feature enhancement module. Next, a deletion diagnostics procedure is conducted to model relations of these semantic-level representations via perceiving the network outputs and the extracted relations are utilized to guide the semantic-level representations to interact with each other. Finally, the interacted representations are utilized to augment original pixel-level representations for final predictions. Extensive experiments are conducted to validate the effectiveness of IDRNet quantitatively and qualitatively. Notably, our intervention-driven context scheme brings consistent performance improvements to state-of-the-art segmentation frameworks and achieves competitive results on popular benchmark datasets, including ADE20K, COCO-Stuff, PASCAL-Context, LIP, and Cityscapes.

Deep Learning/Attention Mechanisms

Amirkeivan Mohtashami, Martin Jaggi

While Transformers have shown remarkable success in natural language processing, their attention mechanism's large memory requirements have limited their ability to handle longer contexts. Prior approaches, such as recurrent memory or retrieval-based augmentation, have either compromised the random-access flexibility of attention (i.e., the capability to select any token in the entire context) or relied on separate mechanisms for relevant context retrieval, which may not be compatible with the model's attention. In this paper, we present a novel approach that allows access to the complete context while retaining random-access flexibility, closely resembling running attention on the entire context. Our method uses a landmark token to represent each block of the input and trains the attention to use it for selecting relevant blocks, enabling retrieval of blocks directly through the attention mechanism instead of by relying on a separate mechanism. Our approach seamlessly integrates with specialized data structures and the system's memory hierarchy, enabling processing of arbitrarily long context lengths. We demonstrate that our method can obtain comparable performance with Transformer-XL while significantly reducing the number of retrieved tokens in each step. Finally, we show that fine-tuning LLaMA 7B with our method successfully extends its context length capacity to over 32k tokens, allowing for inference at the context lengths of GPT-4. We release the implementation of landmark attention and the code to reproduce our experiments at https://github.com/epfml/landmark-attention/.

Deep Learning/Attention Mechanisms

Zixuan Jiang, Jiaqi Gu, Hanqing Zhu, David Pan

Transformers have achieved great success in machine learning applications.Normalization techniques, such as Layer Normalization (LayerNorm, LN) and Root Mean Square Normalization (RMSNorm), play a critical role in accelerating and stabilizing the training of Transformers.While LayerNorm recenters and rescales input vectors, RMSNorm only rescales the vectors by their RMS value.Despite being more computationally efficient, RMSNorm may compromise the representation ability of Transformers.There is currently no consensus regarding the preferred normalization technique, as some models employ LayerNorm while others utilize RMSNorm, especially in recent large language models.It is challenging to convert Transformers with one normalization to the other type.While there is an ongoing disagreement between the two normalization types,we propose a solution to unify two mainstream Transformer architectures, Pre-LN and Pre-RMSNorm Transformers.By removing the inherent redundant mean information in the main branch of Pre-LN Transformers, we can reduce LayerNorm to RMSNorm, achieving higher efficiency.We further propose the Compressed RMSNorm (CRMSNorm) and Pre-CRMSNorm Transformer based on a lossless compression of the zero-mean vectors.We formally establish the equivalence of Pre-LN, Pre-RMSNorm, and Pre-CRMSNorm Transformer variants in both training and inference.It implies that Pre-LN Transformers can be substituted with Pre-(C)RMSNorm counterparts at almost no cost, offering the same arithmetic functionality along with free efficiency improvement.Experiments demonstrate that we can reduce the training and inference time of Pre-LN Transformers by 1% - 10%.

Deep Learning/Attention Mechanisms

Jerry Yao-Chieh Hu, Donglin Yang, Dennis Wu, Chenwei Xu, Bo-Yu Chen, Han Liu

We introduce the sparse modern Hopfield model as a sparse extension of the modern Hopfield model.Like its dense counterpart, the sparse modern Hopfield model equips a memory-retrieval dynamics whose one-step approximation corresponds to the sparse attention mechanism. Theoretically, our key contribution is a principled derivation of a closed-form sparse Hopfield energy using the convex conjugate of the sparse entropic regularizer.Building upon this, we derive the sparse memory retrieval dynamics from the sparse energy function and show its one-step approximation is equivalent to the sparse-structured attention.Importantly, we provide a sparsity-dependent memory retrieval error bound which is provably tighter than its dense analog.The conditions for the benefits of sparsity to arise are therefore identified and discussed.In addition, we show that the sparse modern Hopfield model maintains the robust theoretical properties of its dense counterpart, including rapid fixed point convergence and exponential memory capacity.Empirically, we use both synthetic and real-world datasets to demonstrate that the sparse Hopfield model outperforms its dense counterpart in many situations.

Deep Learning/Attention Mechanisms

Xiaolei Ru, XINYA ZHANG, Zijia Liu, Jack Murdoch Moore, Gang Yan

We consider the problem of reconstructing coupled networks (e.g., biological neural networks) connecting large numbers of variables (e.g.,nerve cells), of which state evolution is governed by dissipative dynamics consisting of strong self-drive (dominants the evolution) and weak coupling-drive. The core difficulty is sparseness of coupling effect that emerges (the coupling force is significant) only momentarily and otherwise remains quiescent in time series (e.g., neuronal activity sequence). Here we learn the idea from attention mechanism to guide the classifier to make inference focusing on the critical regions of time series data where coupling effect may manifest. Specifically, attention coefficients are assigned autonomously by artificial neural networks trained to maximise the Attentive Transfer Entropy (ATEn), which is a novel generalization of the iconic transfer entropy metric. Our results show that, without any prior knowledge of dynamics, ATEn explicitly identifies areas where the strength of coupling-drive is distinctly greater than zero. This innovation substantially improves reconstruction performance for both synthetic and real directed coupling networks using data generated by neuronal models widely used in neuroscience.

Deep Learning/Attention Mechanisms

Bingbin Liu, Jordan Ash, Surbhi Goel, Akshay Krishnamurthy, Cyril Zhang

Why do large language models sometimes output factual inaccuracies and exhibit erroneous reasoning? The brittleness of these models, particularly when executing long chains of reasoning, currently seems to be an inevitable price to pay for their advanced capabilities of coherently synthesizing knowledge, pragmatics, and abstract thought. Towards making sense of this fundamentally unsolved problem, this work identifies and analyzes the phenomenon of _attention glitches_, in which the Transformer architecture's inductive biases intermittently fail to capture robust reasoning. To isolate the issue, we introduce _flip-flop language modeling_ (FFLM), a parametric family of synthetic benchmarks designed to probe the extrapolative behavior of neural language models. This simple generative task requires a model to copy binary symbols over long-range dependencies, ignoring the tokens in between. We find that Transformer FFLMs suffer from a long tail of sporadic reasoning errors, some of which we can eliminate using various regularization techniques. Our preliminary mechanistic analyses show why the remaining errors may be very difficult to diagnose and resolve. We hypothesize that attention glitches account for (some of) the closed-domain hallucinations in natural LLMs.

Deep Learning/Attention Mechanisms

Albert Tseng, Tao Yu, Toni Liu, Christopher De Sa

Attention networks such as transformers have achieved state-of-the-art performance in many domains. These networks rely heavily on the dot product attention operator, which computes the similarity between two points by taking their inner product.However, the inner product does not explicitly model the complex structural properties of real world datasets, such as hierarchies between data points.To remedy this, we introduce cone attention, a drop-in replacement for dot product attention based on hyperbolic entailment cones.Cone attention associates two points by the depth of their lowest common ancestor in a hierarchy defined by hyperbolic cones, which intuitively measures the divergence of two points and gives a $\textit{hierarchy aware}$ similarity score.We test cone attention on a wide variety of models and tasks and show that it improves task-level performance over dot product attention and other baselines, and is able to match dot-product attention with significantly fewer parameters.Our results suggest that cone attention is an effective way to capture hierarchical relationships when calculating attention.

Deep Learning/Attention Mechanisms

Yu Bai, Fan Chen, Huan Wang, Caiming Xiong, Song Mei

Neural sequence models based on the transformer architecture have demonstrated remarkable \emph{in-context learning} (ICL) abilities, where they can perform new tasks when prompted with training and test examples, without any parameter update to the model. This work first provides a comprehensive statistical theory for transformers to perform ICL. Concretely, we show that transformers can implement a broad class of standard machine learning algorithms in context, such as least squares, ridge regression, Lasso, learning generalized linear models, and gradient descent on two-layer neural networks, with near-optimal predictive power on various in-context data distributions. Using an efficient implementation of in-context gradient descent as the underlying mechanism, our transformer constructions admit mild size bounds, and can be learned with polynomially many pretraining sequences. Building on these ``base'' ICL algorithms, intriguingly, we show that transformers can implement more complex ICL procedures involving \emph{in-context algorithm selection}, akin to what a statistician can do in real life---A \emph{single} transformer can adaptively select different base ICL algorithms---or even perform qualitatively different tasks---on different input sequences, without any explicit prompting of the right algorithm or task. We both establish this in theory by explicit constructions, and also observe this phenomenon experimentally. In theory, we construct two general mechanisms for algorithm selection with concrete examples: pre-ICL testing, and post-ICL validation. As an example, we use the post-ICL validation mechanism to construct a transformer that can perform nearly Bayes-optimal ICL on a challenging task---noisy linear models with mixed noise levels. Experimentally, we demonstrate the strong in-context algorithm selection capabilities of standard transformer architectures.

Deep Learning/Attention Mechanisms

Davoud Ataee Tarzanagh, Yingcong Li, Xuechen Zhang, Samet Oymak

Attention mechanism is a central component of the transformer architecture which led to the phenomenal success of large language models. However, the theoretical principles underlying the attention mechanism are poorly understood, especially its nonconvex optimization dynamics. In this work, we explore the seminal softmax-attention model $f(X)=\langle Xv, \texttt{softmax}(XWp)\rangle$, where $X$ is the token sequence and $(v,W,p)$ are trainable parameters. We prove that running gradient descent on $p$, or equivalently $W$, converges in direction to a max-margin solution that separates *locally-optimal* tokens from non-optimal ones. This clearly formalizes attention as an optimal token selection mechanism. Remarkably, our results are applicable to general data and precisely characterize *optimality* of tokens in terms of the value embeddings $Xv$ and problem geometry. We also provide a broader regularization path analysis that establishes the margin maximizing nature of attention even for nonlinear prediction heads. When optimizing $v$ and $p$ simultaneously with logistic loss, we identify conditions under which the regularization paths directionally converge to their respective hard-margin SVM solutions where $v$ separates the input features based on their labels. Interestingly, the SVM formulation of $p$ is influenced by the support vector geometry of $v$. Finally, we verify our theoretical findings via numerical experiments and provide insights.

Deep Learning/Attention Mechanisms

Amanda Bertsch, Uri Alon, Graham Neubig, Matthew Gormley

Since the proposal of transformers, these models have been limited to bounded input lengths, because of their need to attend to every token in the input. In this work, we propose Unlimiformer: a general approach that wraps any existing pretrained encoder-decoder transformer, and offloads the cross-attention computation to a single $k$-nearest-neighbor ($k$NN) index, while the returned $k$NN distances are the attention dot-product scores. This $k$NN index can be kept on either the GPU or CPU memory and queried in sub-linear time; this way, we can index practically unlimited input sequences, while every attention head in every decoder layer retrieves its top-$k$ keys, instead of attending to every key. We evaluate Unlimiformer on several long-document and book-summarization benchmarks, showing that it can process even **500k** token-long inputs from the BookSum dataset, without any input truncation at test time. We demonstrate that Unlimiformer improves pretrained models such as BART and Longformer by extending them to unlimited inputs without additional learned weights and without modifying their code. Our code and models are publicly available at https://github.com/abertsch72/unlimiformer , and support LLaMA-2 as well.

Deep Learning/Attention Mechanisms

Yingyi Chen, Qinghua Tao, Francesco Tonin, Johan Suykens

Recently, a new line of works has emerged to understand and improve self-attention in Transformers by treating it as a kernel machine. However, existing works apply the methods for symmetric kernels to the asymmetric self-attention, resulting in a nontrivial gap between the analytical understanding and numerical implementation. In this paper, we provide a new perspective to represent and optimize self-attention through asymmetric Kernel Singular Value Decomposition (KSVD), which is also motivated by the low-rank property of self-attention normally observed in deep layers. Through asymmetric KSVD, i) a primal-dual representation of self-attention is formulated, where the optimization objective is cast to maximize the projection variances in the attention outputs; ii) a novel attention mechanism, i.e., Primal-Attention, is proposed via the primal representation of KSVD, avoiding explicit computation of the kernel matrix in the dual; iii) with KKT conditions, we prove that the stationary solution to the KSVD optimization in Primal-Attention yields a zero-value objective. In this manner, KSVD optimization can be implemented by simply minimizing a regularization loss, so that low-rank property is promoted without extra decomposition. Numerical experiments show state-of-the-art performance of our Primal-Attention with improved efficiency. Moreover, we demonstrate that the deployed KSVD optimization regularizes Primal-Attention with a sharper singular value decay than that of the canonical self-attention, further verifying the great potential of our method. To the best of our knowledge, this is the first work that provides a primal-dual representation for the asymmetric kernel in self-attention and successfully applies it to modelling and optimization.

Deep Learning/Attention Mechanisms

Kaiyue Wen, Yuchen Li, Bingbin Liu, Andrej Risteski

Transformer interpretability aims to understand the algorithm implemented by a learned Transformer by examining various aspects of the model, such as the weight matrices or the attention patterns.In this work, through a combination of theoretical results and carefully controlled experiments on synthetic data, we take a critical viewof methods that exclusively focus on individual parts of the model, rather than consider the network as a whole.We consider a simple synthetic setup of learning a (bounded) Dyck language. Theoretically, we show that the set of models that (exactly or approximately) solve this task satisfy a structural characterization derived from ideas in formal languages (the pumping lemma).We use this characterization to show that the set of optima is qualitatively rich; in particular, the attention pattern of a single layer can be "nearly randomized", while preserving the functionality of the network.We also show via extensive experiments that these constructions are not merely a theoretical artifact: even with severe constraints to the architecture of the model, vastly different solutions can be reached via standard training. Thus, interpretability claims based on inspecting individual heads or weight matrices in the Transformer can be misleading.

Deep Learning/Attention Mechanisms

Wenchong He, Zhe Jiang, Tingsong Xiao, Zelin Xu, Shigang Chen, Ronald Fick, MILES MEDINA, Christine Angelini

Transformers are widely used deep learning architectures. Existing transformers are mostly designed for sequences (texts or time series), images or videos, and graphs. This paper proposes a novel transformer model for massive (up to a million) point samples in continuous space. Such data are ubiquitous in environment sciences (e.g., sensor observations), numerical simulations (e.g., particle-laden flow, astrophysics), and location-based services (e.g., POIs and trajectories). However, designing a transformer for massive spatial points is non-trivial due to several challenges, including implicit long-range and multi-scale dependency on irregular points in continuous space, a non-uniform point distribution, the potential high computational costs of calculating all-pair attention across massive points, and the risks of over-confident predictions due to varying point density. To address these challenges, we propose a new hierarchical spatial transformer model, which includes multi-resolution representation learning within a quad-tree hierarchy and efficient spatial attention via coarse approximation. We also design an uncertainty quantification branch to estimate prediction confidence related to input feature noise and point sparsity. We provide a theoretical analysis of computational time complexity and memory costs. Extensive experiments on both real-world and synthetic datasets show that our method outperforms multiple baselines in prediction accuracy and our model can scale up to one million points on one NVIDIA A100 GPU. The code is available at https://github.com/spatialdatasciencegroup/HST

Deep Learning/Attention Mechanisms

Sivaramakrishnan Swaminathan, Antoine Dedieu, Rajkumar Vasudeva Raju, Murray Shanahan, Miguel Lazaro-Gredilla, Dileep George

In-context learning (ICL) is one of the most powerful and most unexpected capabilities to emerge in recent transformer-based large language models (LLMs). Yet the mechanisms that underlie it are poorly understood. In this paper, we demonstrate that comparable ICL capabilities can be acquired by an alternative sequence prediction learning method using clone-structured causal graphs (CSCGs). Moreover, a key property of CSCGs is that, unlike transformer-based LLMs, they are {\em interpretable}, which considerably simplifies the task of explaining how ICL works. Specifically, we show that it uses a combination of (a) learning template (schema) circuits for pattern completion, (b) retrieving relevant templates in a context-sensitive manner, and (c) rebinding of novel tokens to appropriate slots in the templates. We go on to marshall evidence for the hypothesis that similar mechanisms underlie ICL in LLMs. For example, we find that, with CSCGs as with LLMs, different capabilities emerge at different levels of overparameterization, suggesting that overparameterization helps in learning more complex template (schema) circuits. By showing how ICL can be achieved with small models and datasets, we open up a path to novel architectures, and take a vital step towards a more general understanding of the mechanics behind this important capability.